COVID-19 Progression

Introduction

library(tidyverse)
library(magrittr)
library(lubridate)
library(scales)
library(matrixStats)
library(ggrepel)
library(broom)
library(glue)
library(jsonlite)
library(pander)
library(plotly)
panderOptions("big.mark", ",")
panderOptions("table.split.table", Inf)
panderOptions("table.style", "rmarkdown")
theme_set(theme_bw())

Disclaimer: This very simple report was prepared by a bioinformatician with no experience in epidemiology or virology, and as such should be treated simply as an alternate viewpoint on the data, which I was simply unable to find elsewhere. Many other people exist with much greater expertise on this subject. However, I do hope this provides a useful perspective which is able to add constructively to the wider discussion. In addition, it should be noted that this is very much focussed on Australian data.

confirmed <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Confirmed.csv") %>%
    read_csv() %>%
    pivot_longer(
        cols = ends_with("20"),
        names_to = "date",
        values_to = "confirmed"
    )  %>%
    mutate(
        date = str_replace_all(
            date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
        ) %>%
            ymd()
    ) %>%
    dplyr::rename(
        Country = `Country/Region`
    ) %>%
    dplyr::mutate(
        Country = case_when(
            `Province/State` == "Hubei" ~ "China (Hubei)",
            `Province/State` == "Hong Kong" ~ "Hong Kong",
            grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
            !grepl("China", Country) ~ Country
        )
    ) %>%
    dplyr::filter(
        !is.na(confirmed)
    ) 

latestAU <- fromJSON("https://api.infotorch.org/api/covid19/totals/") %>%
  as_tibble() %>%
  rename(
    `Province/State` = state_long,
    date = date_updated
  ) %>%
  mutate(
    date = ymd(date),
    Country = "Australia",
    `Province/State` = str_replace_all(
      `Province/State`, "ACT", "Australian Capital Territory"
    )
  ) %>%
  dplyr::filter(
    !str_detect(`Province/State`, "Total")
  ) %>%
  dplyr::select(
    any_of(colnames(confirmed)), deaths, tested
  ) %>%
  mutate(
    date = max(date)
  )
# Update the AU records if there are any timepoints
# on days beyond the last value provided by JHU
updateAU <- max(latestAU$date) >
  max(
    dplyr::filter(confirmed, Country == "Australia")$date
    )
if (updateAU) {
  confirmed %<>%
    bind_rows(
      dplyr::select(latestAU, any_of(colnames(.)))
    )
  n <- fromJSON("https://api.infotorch.org/api/covid19/totals/") %>%
    dplyr::filter(date_updated == max(date_updated), state != "AU") %>% 
    nrow()
}

recovered <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Recovered.csv") %>%
  read_csv() %>%
  pivot_longer(
    cols = ends_with("20"),
    names_to = "date",
    values_to = "recovered"
  )  %>%
  mutate(
    date = str_replace_all(
      date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
    ) %>%
      ymd()
  ) %>%
  dplyr::rename(
    Country = `Country/Region`
  ) %>%
  dplyr::mutate(
    Country = case_when(
      `Province/State` == "Hubei" ~ "China (Hubei)",
      `Province/State` == "Hong Kong" ~ "Hong Kong",
      grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
      !grepl("China", Country) ~ Country
    )
  )
deaths <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Deaths.csv") %>%
  read_csv() %>%
  pivot_longer(
    cols = ends_with("20"),
    names_to = "date",
    values_to = "deaths"
  )  %>%
  mutate(
    date = str_replace_all(
      date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
    ) %>%
      ymd()
  ) %>%
  dplyr::rename(
    Country = `Country/Region`
  ) %>%
  dplyr::mutate(
    Country = case_when(
      `Province/State` == "Hubei" ~ "China (Hubei)",
      `Province/State` == "Hong Kong" ~ "Hong Kong",
      grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
      !grepl("China", Country) ~ Country
    )
  )

# No recoveries are reported in the latestAU data
# Assume values are identical
if (updateAU){
  deaths %<>%
    bind_rows(
      dplyr::select(latestAU, any_of(colnames(.)))
    )
  recovered %<>%
    bind_rows(
      dplyr::select(latestAU, any_of(colnames(.)))
      ) %>% 
    arrange(`Province/State`, Country, date) %>%
    mutate(recovered = zoo::na.locf(recovered))
}

Data was sourced from Johns Hopkins University (https://coronavirus.jhu.edu/), using the datasets provided by JHU at https://github.com/CSSEGISandData/COVID-19. JHU data is updated every 24 hours at approximately 23:59(UTC), which is about 10:30AM in Adelaide.

The official government figures at www.health.gov.au appear to lag media reports, likely to ensure accuracy of the official numbers. The official Australian numbers are not used for this analysis, instead relying on those provided by JHU, given that JHU are extremely careful and comprehensive in their sourcing of numbers. A significant disparity is not expected. Live updates for Australia are available from https://covid-19-au.github.io/ for those who would like an up to the minute breakdown of confirmed cases. The current Australian numbers used in all plots below do contain any cases reported since the JHU dataset was updated. As such, the latest values for infection rate may be incomplete for today as all states may not yet have reported. 5 states/territories have currently reported updated figures since the overnight JHU release.

Population sizes for the most impacted countries were manually obtained from https://www.worldometers.info/ and should not be considered as authoritative. Given the disparity of infection within China, China was broken into Hubei Province, Hong Kong and the rest of China. As an open acknowledgement of the crudeness of population values, population estimates for Hubei Province were taken from the 2018 estimates given by Statista.com. This particular population estimate is likely to be low, and as a result confirmed case rates for Hubei province may be an overestimate, and consequently, confirmed case rates for the rest of China may also be an underestimate.

Confirmed cases of COVID-19 as provided by the Chinese Government have been discussed elsewhere as unusual, and data appears potentially unreliable. In this analysis, discussions regarding accurate Chinese reporting are not considered further and data is simply presented as supplied by JHU.

However, all countries are likely to contain many unreported cases given the incomplete testing regimes in place for most countries. Similarly, reporting in many countries may have features that cause concerns regarding data integrity and this makes comparison across countries difficult.

hb <- 59170000
pops <- tribble(
    ~Country, ~Population, ~Region,
    "Australia", 25499884, "Oceania",
    "Austria", 9006398, "Europe",
    "Belgium", 11575214, "Europe",
    "Brazil", 212129490, "South America",
    "Canada", 37742154, "North America",
    "Chile", 19068026, "South America",
    "China (Hubei)", hb, "Asia",
    "China (Other)", 1408526449 - hb, "Asia",
    "Czechia", 10703010, "Europe",
    "Denmark", 5786274, "Europe",
    "Ecuador", 17564089, "South America",
    "Finland", 5538181, "Europe",
    "France", 65273511, "Europe",
    "Germany", 83783942, "Europe",
    "Greece", 10423054, "Europe",
    "Hong Kong", 7479307, "Asia",
    "Iceland", 364260, "Europe",
    "Indonesia", 272702678, "Asia",
    "Italy", 60486925, "Europe",
    "Iran", 83677594, "Middle East",
    "Ireland", 4921810, "Europe",
    "Israel", 8615601, "Middle East",
    "Japan", 126476461, "Asia",
    "Jordan", 10174146, "Middle East",
    "Korea, South", 51269185, "Asia",
    "Luxembourg", 613894, "Europe",
    "Malaysia", 32245488, "Asia",
    "Netherlands", 17134872, "Europe",
    "New Zealand", 4811065, "Oceania",
    "Norway", 5408930, "Europe",
    "Pakistan",  219629013, "Asia",
    "Poland", 37858096, "Europe",
    "Portugal", 10196709, "Europe",
    "Qatar", 2866531, "Middle East",
    "Russia", 145917069, "Europe",
    "Singapore", 5836728, "Asia",
    "Spain", 46754778, "Europe",
    "Sweden", 10081035, "Europe",
    "Switzerland", 8654622, "Europe",
    "Taiwan*", 23804524, "Asia",
    "Turkey", 84081383, "Europe",
    "United Arab Emirates", 9856053, "Middle East", 
    "United Kingdom", 67886011, "Europe",
    "US", 331002651, "North America"
)

International Data

Table of Most Impacted Countries

All information presented in this section is effectively the cumulative, confirmed incidence rate. Recovered patients and those who have passed away are still included in these numbers. Testing rates and results are also not included, and these may be highly informative if able to be sourced accurately.

minPop <- 4e6
confirmed %>%
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  group_by(Country) %>%
  dplyr::filter(
    date == max(date),
  ) %>%
  ungroup() %>%
  right_join(pops) %>%
  dplyr::filter(
    Population > minPop
  ) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>%
  arrange(desc(rate)) %>%
  dplyr::slice(1:25) %>%
  mutate(
    rate = sprintf("%.1f", rate),
    Population = comma(Population)
  ) %>%
  rename_at(vars(everything()), str_to_title) %>%
  dplyr::select(
    Country, Date, Confirmed, Population, Rate
  ) %>%
  rename(`Rate (Cases per Million)` = Rate) %>%
  pander(
    justify = "lrrrr",
    caption = paste(
      "The", nrow(.), "most impacted countries studied here and shown as a proportion of total population.",
      "Only countries with a population greater than",
      comma(minPop), "are shown.",
      "The final column provides the latest confirmed infection rate as cases per million people.",
      "Whilst the virus spreads with no regard to population size, the rate as shown here indicates the __degree of stress which each country's health-care system is likely to be experiencing__.",
      "Several countries shown here have not attracted much media attention due lower case numbers than China and Italy, but are likely to be experiencing significant duress."
    )
  )

The 25 most impacted countries studied here and shown as a proportion of total population. Only countries with a population greater than 4,000,000 are shown. The final column provides the latest confirmed infection rate as cases per million people. Whilst the virus spreads with no regard to population size, the rate as shown here indicates the degree of stress which each country’s health-care system is likely to be experiencing. Several countries shown here have not attracted much media attention due lower case numbers than China and Italy, but are likely to be experiencing significant duress.

Country	Date	Confirmed	Population	Rate (Cases per Million)
China (Hubei)	2020-03-21	67,800	59,170,000	1145.9
Italy	2020-03-21	53,578	60,486,925	885.8
Switzerland	2020-03-21	6,575	8,654,622	759.7
Spain	2020-03-21	25,374	46,754,778	542.7
Norway	2020-03-21	2,118	5,408,930	391.6
Austria	2020-03-21	2,814	9,006,398	312.4
Germany	2020-03-21	22,213	83,783,942	265.1
Iran	2020-03-21	20,610	83,677,594	246.3
Denmark	2020-03-21	1,420	5,786,274	245.4
Belgium	2020-03-21	2,815	11,575,214	243.2
France	2020-03-21	14,431	65,273,511	221.1
Netherlands	2020-03-21	3,640	17,134,872	212.4
Sweden	2020-03-21	1,763	10,081,035	174.9
Korea, South	2020-03-21	8,799	51,269,185	171.6
Ireland	2020-03-21	785	4,921,810	159.5
Portugal	2020-03-21	1,280	10,196,709	125.5
Israel	2020-03-21	883	8,615,601	102.5
Finland	2020-03-21	523	5,538,181	94.4
Czechia	2020-03-21	995	10,703,010	93.0
US	2020-03-21	25,489	331,002,651	77.0
United Kingdom	2020-03-21	5,067	67,886,011	74.6
Singapore	2020-03-21	432	5,836,728	74.0
Greece	2020-03-21	530	10,423,054	50.8
Australia	2020-03-22	1,266	25,499,884	49.6
Malaysia	2020-03-21	1,183	32,245,488	36.7

Cumulative Incidence Rates

startingPoint <- 4
minDays <- 5
# Use Singapore as that has the longest dataset besides Hubei
nDays <- confirmed %>%
  dplyr::filter(Country == "Singapore") %>% 
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  left_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>% 
  dplyr::filter(rate > startingPoint) %>% 
  nrow() %>%
  subtract(1)

refRate <- c(2, 4, 8)
p <- confirmed %>%
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  right_join(
    dplyr::filter(pops, Population > minPop)
  ) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>%
  dplyr::filter(
    rate > startingPoint
  ) %>%
  group_by(Country) %>%
  mutate(
    days = date - min(date)
  ) %>%
  dplyr::filter(
    max(days) >= minDays
  ) %>%
  ungroup() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  arrange(date) %>%
  mutate(Country = fct_inorder(Country)) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(Days, Rate, colour = Country, Date = Date, Confirmed = Confirmed)
  ) +
  geom_segment(
    aes(x, y, xend = xmax, yend = ymax),
    data = tibble(
      x = 0,
      y = startingPoint,
      xmax = c(16, 32, nDays ),
      ymax = startingPoint*2^(xmax / refRate)
    ),
    inherit.aes = FALSE,
    colour = "grey70",
    linetype = 2
  ) +
  geom_text(
        aes(xmax, ymax, label = label),
    data = tibble(
      xmax = c(16, 32, nDays - 2),
      ymax = startingPoint*2^(xmax / refRate),
      label = glue("Doubling in\n {refRate} days")
    ),
    colour = "grey70",
    inherit.aes = FALSE
  ) +
  geom_point() +
  geom_line() +
  scale_x_continuous(
    expand = expand_scale(mult = c(0, 0.05)),
  ) +
  scale_y_log10(
    expand = expand_scale(mult = c(0, 0.05))
  ) +
  xlab(
    paste(
      "Days since passing", 
      startingPoint,
      "confirmed cases/million"
    )
  ) +
  ylab("Confirmed Cumulative Infection Rate (cases/million)")

ggplotly(
  p, 
  tooltip = c(
    "Days", "Rate", "Country", "Date", "Confirmed"
  )) 

COVID-19 Confirmed Cumulative Infection Rate for countries which have exceeded 4 confirmed cases/million for 5 or more days, and with populations greater than 4,000,000. Data is only shown for the first 46 calendar days since passing 4 confirmed cases/million. Note that from the day records begin in this dataset (2020-01-22), the confirmed infection rate in Hubei was 7.5 confirmed cases/million. Diagonal grey lines indicate a doubling in the infection rate every 2, 4, or 8 days. To hide a country, click on the country in the plot legend. Clicking again on the country in the legend will restore the data within the plot. Countries are shown in order of the date at which they passed the 4 confirmed case/million mark. Due to the large number of countries shown, you may need to scroll through the legend. Regions of the plot are also able to be zoomed interactively. Please note the y-axis is shown on the logarithmic scale, so that a series of points which appear to be diagonal will indicate exponential growth. The flatter the line, the slower the growth and a perfectly horizontal line would indicate zero growth, or no new confirmed cases.

All figures and tables presented here simply aim to show an alternative viewpoint on the data. Every way to view COVID-19 data will mask important features, and the values shown here do not take into account vital factors such as population density, variability of infection across regions within countries, social culture and demographics. Many countries may not be directly comparable for a combination of the above factors. It is simply to view the data through the lens of a country’s population size using a value which should be easily interpretable.

In the above plot:

• Only countries are shown where the infection rate has surpassed 4 cases/million. This Cumulative Confirmed Infection Rate equates to about 102 confirmed cases within Australia, and is comparable to the days since passing 100 confirmed cases commonly shown elsewhere.
• This choice seemed to be a useful way of enabling the comparison of COVID-19 progression across countries after scaling for population size

Additionally, Australia’s spread of the virus appears marginally slower than many other countries.

• This may be a reflection of Australian geography or our tendency to have large personal space requirements
• This may also be a reflection of the pre-emptive strategies already being taken by the population and government
• Overall, the Australian infection rate brings mild relief that we are doing a little better than many other countries. However testing rates are far lower than in countries like South Korea and many genuine cases are likely to be undetected and unreported
• Despite the above, Australia is still clearly in the exponential growth phase with no sign of the growth levelling out. Infections are currently doubling in slightly less than 4 days, meaning Australian infections are expected to exceed 2,532 by Thursday 26 March, 2020. If this case rate is not observed, it may be an early sign that distancing measures are beginning to be effective
• Using an estimated population size of 25,499,884, the total percentage of the Australian population confirmed as infected currently sits at 0.005%.

Turning to other countries beyond Australia:

• Only South Korea,and China appear to have brought the virus under some level of control. The infection rate currently sits around 171.6 per million for South Korea and 1145.9 per million for Hubei Province. This can also be thought of as 0.0172% and 0.1146% of the total populations respectively. Note that despite these apparently low percentages, the actual numbers of deaths and hospitalisations are extremely non-trivial and the real impacts of these numbers cannot be treated lightly.
• Japan and UAE’s early measures also appear to be highly effective, however the recent growth in infections within Singapore and Hong Kong should serve as a caution
• Some of the above countries (e.g. Iran) appear to be in the early stages of levelling out, indicating that either the initial exponential growth phase may be ending in these countries, or under-reporting has become rife
• Other countries such as Italy, Switzerland, the Unites States and the UK are clearly still in an exponential growth phase.
• US numbers may also be unreliable given the low rates of testing and numerous anecdotal stories of suspected infections

Currently Active Infections Rates

As an alternative viewpoint, the numbers of recovered and deceased patients have been removed from the above plot to provide an estimate of the currently active infections.

p2 <- confirmed %>%
  dplyr::filter(
    !str_detect(Country, "Other")
  ) %>%
  left_join(recovered) %>%
  left_join(deaths) %>%
    right_join(
      dplyr::filter(pops, Population > minPop)
    ) %>%
  mutate(
    active = confirmed - recovered - deaths
  ) %>%
  dplyr::filter(
    !is.na(active), confirmed > 0
  ) %>%
  group_by(
    Country, Population, date
  ) %>%
  summarise(
    active = sum(active),
    confirmed = sum(confirmed),
    recovered = sum(recovered),
    deaths = sum(deaths)
  ) %>%
  mutate(rate = 1e6 * active / Population) %>%
  dplyr::filter(
    rate > startingPoint
  ) %>%
  mutate(
    days = date - min(date)
  ) %>%
  dplyr::filter(max(days) > minDays) %>%
  ungroup() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  arrange(date) %>%
  mutate(Country = fct_inorder(Country)) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(
      x = Days, y = Rate, colour = Country, 
      Date = Date, Active = Active,
      Confirmed = Confirmed, Recovered = Recovered,
      Deaths = Deaths
      )
  ) +
  geom_segment(
    aes(x, y, xend = xmax, yend = ymax),
    data = tibble(
      x = 0,
      y = startingPoint,
      xmax = c(20.5, 41, nDays),
      ymax = startingPoint + 2^(xmax/ c(2, 4, 8))
    ),
    inherit.aes = FALSE,
    colour = "grey70",
    linetype = 2
  ) + 
  geom_text(
        aes(xmax, ymax, label = label),
    data = tibble(
      xmax = c(20.5, 41, nDays),
      rate = c(2, 4, 8),
      ymax = 2^(xmax/ rate),
      label = glue("Double in\n {rate} days")
    ),
    colour = "grey70",
    inherit.aes = FALSE
  ) +
  geom_point() +
  geom_line() +
  scale_x_continuous(
    expand = expand_scale(mult = c(0, 0.05)),
  ) +
  scale_y_log10(
    expand = expand_scale(mult = c(0, 0.05))
  ) +
  xlab(
    paste(
      "Days since passing", 
      startingPoint, 
      "confirmed active cases/million"
    )
  ) +
  ylab("Confirmed Active Infection Rate (cases/million)")

ggplotly(p2) 

Confirmed active cases of COVID-19 for countries where the confirmed infection rate has exceeded 4 confirmed active cases/million for more than 46 calendar days. Only countries with a population greater than 4,000,000 are shown for better visualisation. Due to difficulties introduced by the currently reported low active infection rate outside Hubei province, data from China has been excluded from this plot, with the exception of Hubei and Hong Kong. To hide a country, click on the country in the plot legend. Clicking again on the country in the legend will restore the data within the plot. Countries are shown in order of the date at which they passed the 4 confirmed active case/million mark. Due to the number of countries shown, you may need to scroll through the legend. Regions of the plot are also able to be zoomed interactively. Please note the y-axis is shown on the logarithmic scale, so that a series of points which appear to be diagonal will indicate exponential growth/decay. Given the different starting point to the previous plot, data will generally be shown for fewer time-points.

Notable features of this perspective are:

• Active infection rates in South Korea are currently either declining or stable
• According to these figures, active infections within Hubei province are also significantly declining
• Despite strict control measures, active infection rates are exponentially increasing in both Hong Kong and Singapore

Dimensional Reduction

In order to summarise which countries are the most similar to each other, a Principal Component Analysis was performed. This enables the multi-dimensional data of the above plots to summarised in two dimensions. As missing data cannot be included in this analysis, several countries which are at earlier comparative time-points than Australia were omitted from this analysis.

nDays <- confirmed %>% 
  dplyr::filter(Country == "Australia") %>% 
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  left_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>% 
  dplyr::filter(rate > startingPoint) %>% 
  nrow() %>%
  subtract(1)

pca <- confirmed %>%
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  right_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>%
  dplyr::filter(
    rate > startingPoint,
    Population > minPop
  ) %>%
  group_by(Country) %>%
  mutate(
    days = date - min(date)
  ) %>%
  dplyr::filter(
    max(days) >= nDays
  ) %>%
  ungroup() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  dplyr::select(Country, rate, days) %>%
  pivot_wider(
    values_from = rate,
    names_from = days
  ) %>%
  as.data.frame() %>%
  column_to_rownames("Country") %>%
  as.matrix() %>%
  .[!rowAnyNAs(.),] %>%
  log() %>%
  prcomp() 

set.seed(101)
pca$x %>%
  as.data.frame() %>%
  rownames_to_column("Country") %>%
  mutate(
    Cluster = cbind(PC1, PC2) %>%
      kmeans(k) %>%
      .[["cluster"]] %>%
      as.factor()
  ) %>%
  ggplot(aes(PC1, PC2, label = Country, colour = Cluster)) +
  geom_point() +
  geom_text_repel(
    show.legend = FALSE
  ) +
  stat_ellipse(
    aes(fill = Cluster),
    colour = NA,
    geom = "polygon",
    alpha = 0.1
    ) +
  xlab(
    paste0(
      "PC1 (", pcPercent[['PC1']],")"
      )
  ) +
    ylab(
    paste0(
      "PC2 (", pcPercent[['PC2']], ")"
      )
  ) +
  theme(
    legend.position = "none"
  )

Dimensional reduction showing which countries infection rates are the most similar to each other at the 12 day mark since passing 4 confirmed cases/million. This may or may not be indicative of future spread within the population. The value 12 days was simply chosen as this marks how long since Australia passed this threshold Countries which have not progressed beyond 4 confirmed cases/million for 12 days or more are not shown. Countries with populations < 4,000,000 are also excluded. Clusters were generated using k-means, manually specifying k = 2 and are not definitive. Principal Component 1, on the x-axis, corresponds to the greatest source of variability within the data (92.9%), and countries which appear near each other along this axis can be assumed to be showing similar growth in confirmed infection rates at this time point. Separation along the y-axis is less significant, but also worthy of note, as this represents 3.2% of variability within the data. At this early point, Australia’s cumulative, confirmed infection rate is diverging from the cluster of countries which have responded well and is becoming more similar to Israel, the UK and other poor responding countries. This is suggestive that the early measures instituted in Australia may have been inadequate.

Fatality, Recovery and Active Infection Rates

Summary of All Rates

fr <- confirmed %>%
  inner_join(deaths) %>%
  group_by(Country) %>%
  dplyr::filter(date == max(date)) %>%
  ungroup() %>%
  summarise(fr = sum(deaths) / sum(confirmed)) %>%
  .[["fr"]]
rr <- confirmed %>%
  inner_join(recovered) %>%
  group_by(Country) %>%
  dplyr::filter(date == max(date)) %>%
  ungroup() %>%
  summarise(rr = sum(recovered) / sum(confirmed)) %>%
  .[["rr"]]

Summarising all available data from all countries:

• The current fatality rate is 4.3%. This may be a function of under-reporting of true cases and is likely to be an overestimate.
• The current recovery rate is 30.0%. Given the level of under-reporting this may also be highly inaccurate.
• At this point, 65.7% of all confirmed infections are considered as ‘active’.

p4 <-
  confirmed %>%
  group_by(Country) %>%
  dplyr::filter(date == max(date)) %>%
  summarise(
    confirmed = sum(confirmed)
  ) %>%
  right_join(pops) %>%
  dplyr::filter(
    1e6*confirmed / Population > startingPoint,
    Country != "Cruise Ship"
  ) %>%   
  left_join(
    recovered %>%
      group_by(Country) %>%
      dplyr::filter(date == max(date)) %>%
      summarise(
        recovered = sum(recovered)
      )
  ) %>%
  left_join(
    deaths %>%
      group_by(Country) %>%
      dplyr::filter(date == max(date)) %>%
      summarise(
        deaths = sum(deaths)
      )
  ) %>%
  mutate(
    active = confirmed - recovered - deaths
  ) %>%
  mutate(
    active = 100*active / confirmed,
    recovered = 100*recovered / confirmed,
    fatalities = 100*deaths / confirmed
  ) %>%
  dplyr::filter(active < 100) %>%
  arrange(desc(confirmed)) %>%
  mutate(Country = fct_inorder(Country)) %>%
  pivot_longer(
    cols = c(active, recovered, fatalities),
    names_to = "Status",
    values_to = "Percentage"
  ) %>%
  mutate(
    Status = str_to_title(Status),
    Status = factor(
      Status, 
      levels = c("Active", "Recovered", "Fatalities")
    ),
    Percentage = round(Percentage, 2)
  ) %>%
  mutate(confirmed = comma(confirmed)) %>%
  rename(Confirmed = confirmed) %>%
  ggplot(
    aes(
      Country, Percentage,
      fill = Status, cases = Confirmed
    )
  ) +
  geom_col() +
  scale_fill_manual(
    values = c(
      Active = "blue",
      Recovered = "green",
      Fatalities = "red"
      )
  ) +
  scale_y_continuous(expand = expand_scale(0, 0)) +
  coord_flip() +
  labs(x = c()) +
  theme(
    legend.position = "none"
  )

ggplotly(p4)

Fatality, Recovery and Active Infection rates for countries which have exceeded 4 confirmed cases / million. Countries are shown in order of the number of confirmed cases.

Fatality Rate Vs Time

plotFr <- confirmed %>%
  inner_join(deaths) %>%
  group_by(Country, date) %>%
  summarise_at(
    vars(confirmed, deaths),
    sum
  ) %>%
  right_join(pops) %>%
  ungroup() %>%
  mutate(
    `Infection Rate` = 1e6 * confirmed / Population
  ) %>%
  dplyr::filter(
    `Infection Rate` > startingPoint
    ) %>%
  group_by(Country) %>%
  mutate(
    Days = date - min(date),
    n = n()
  ) %>%
  dplyr::filter(
    n > minDays,
    max(deaths) > 0
    ) %>%
  ungroup() %>%
  arrange(desc(n)) %>%
  mutate(
    Country = fct_inorder(Country),
    Rate = deaths / confirmed,
    Days = as.integer(Days),
    `Fatality Rate` = percent(Rate, accuracy = 0.1)
  ) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(
      x = Days, y = Country, fill = Rate,
      conf = Confirmed, 
      deaths = Deaths,
      date = Date,
      label = `Fatality Rate`
      )
  ) +
  geom_raster() +
  scale_fill_viridis_c(
    option = "magma",
    breaks = seq(0, 0.08, by = 0.02)
  ) +
  scale_x_continuous(expand = expand_scale(0, 0)) +
  scale_y_discrete(expand = expand_scale(0, 0)) +
  labs(
    x = glue(
      "Days since passing {startingPoint} cases/million"
    ),
    y = c(),
    fill = "Fatality\nRate"
  ) +
  theme(
    panel.grid = element_blank()
  )

cpFr <- glue(
  "*Fatality Rate for confirmed cases after passing {startingPoint} confirmed cases / million.
  Only countries with {minDays} days of data beyond this time-point are shown, and are shown in order of the date at which they passed this threshold.
  Countries with no recorded fatalities have been excluded. 
  A clear trend of an increasing fatality rate with time is evident in many countries (e.g. Spain, France, Italy, UK), however for some countries at the bottom of this plot (e.g. Singapore), this rate appears relatively stable throughout the majority of days.
  The overall Fatality Rate for confirmed cases is currently ({percent(fr, accuracy = 0.1)}).*"
)

ggplotly(
  plotFr,
  tooltip = c(
    "Country", "Date", "Days", "Confirmed", "Deaths", 
    "Fatality Rate"
    )
  )

Fatality Rate for confirmed cases after passing 4 confirmed cases / million. Only countries with 5 days of data beyond this time-point are shown, and are shown in order of the date at which they passed this threshold. Countries with no recorded fatalities have been excluded. A clear trend of an increasing fatality rate with time is evident in many countries (e.g. Spain, France, Italy, UK), however for some countries at the bottom of this plot (e.g. Singapore), this rate appears relatively stable throughout the majority of days. The overall Fatality Rate for confirmed cases is currently (4.3%).

Recoveries Vs Fatalities Vs Time

p6 <- confirmed %>%
  inner_join(deaths) %>%
  inner_join(recovered) %>%
  group_by(Country, date) %>%
  summarise_at(
    vars(confirmed, recovered, deaths),
    sum
  ) %>%
  ungroup() %>%
  right_join(pops) %>%
  mutate(
    active = confirmed - deaths - recovered,
    `Infection Rate` = 1e6 * confirmed / Population
  ) %>%
  dplyr::filter(
    `Infection Rate` > startingPoint,
    Country != "Cruise Ship"
  ) %>%
  group_by(Country) %>%
  mutate(
    Days = date - min(date)
  ) %>%
  dplyr::filter(
    max(Days) > minDays
  ) %>%
  ungroup() %>%
  mutate(
    ratio = round(log2(recovered / deaths), 2)
  ) %>%
  dplyr::filter(
    !is.infinite(ratio),
    !is.na(ratio)
  ) %>%
  arrange(desc(Days)) %>%
  mutate(Country = fct_inorder(Country)) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(
      x = Days, y = Country, fill = Ratio,
      conf = Confirmed, 
      rec = Recovered,
      deaths = Deaths,
      date = Date,
    )
  ) +
  geom_raster() +
  scale_fill_gradient2(
    low = "red", high = "green", na.value = "grey80"
  ) +
  scale_x_continuous(
    expand = expand_scale(0, 0)
  ) +
  scale_y_discrete(
    expand = expand_scale(0, 0)
  ) +
  labs(
    x = glue(
      "Days since passing {startingPoint} cases/million"
    ),
    y = c(),
    fill = "Ratio"
  ) +
  theme(
    panel.grid = element_blank()
  )

cp6 <- glue(
  "*Comparison of recoveries and fatalities as a time course, beginning at the day cases exceeded {startingPoint} confirmed cases / million.
  Countries are only shown if data is available for more than {minDays} days since passing this threshold.
  The ratio of recoveries to fatalities is shown on the log~2~ scale, such that when fatalities outnumber recoveries, the colour become more red.
  Conversely if the recoveries outnumber the fatalities the colour will become more green.
  If these two numbers are approximately equal, the colour will be white.
  As the numbers are on the log~2~ scale, a ratio of 2, would indicate 2^2^ = 4 times the number of __recoveries to fatalities__.
  Similarly a ratio of -2 would indicate that fatalities outnumber recoveries by a factor of 2^2^ = 4.
  Ratios are only available once there is one or more confirmed recoveries in addition to one or more confirmed fatalities.*"
)

A time-course of the relationship between recoveries and fatalities is shown. Series of days which extend deeply into the red may possibly indicate where medical facilities are overloaded. However, it is possible that during these times more attention is focussed on keeping critically ill patients alive than confirming a recovery. It should be noted that many of the countries which are deep into the red at the current time are affluent Western countries. It is also worth noting that despite the high death toll in Italy, recoveries outnumber fatalities for the majority of this time-course.

ggplotly(p6)

Comparison of recoveries and fatalities as a time course, beginning at the day cases exceeded 4 confirmed cases / million. Countries are only shown if data is available for more than 5 days since passing this threshold. The ratio of recoveries to fatalities is shown on the log₂ scale, such that when fatalities outnumber recoveries, the colour become more red. Conversely if the recoveries outnumber the fatalities the colour will become more green. If these two numbers are approximately equal, the colour will be white. As the numbers are on the log₂ scale, a ratio of 2, would indicate 2² = 4 times the number of recoveries to fatalities. Similarly a ratio of -2 would indicate that fatalities outnumber recoveries by a factor of 2² = 4. Ratios are only available once there is one or more confirmed recoveries in addition to one or more confirmed fatalities.

Australian Specific Data

Australian State populations were taken from the ABS Website and were accurate in Sept 2019. The difference with previous estimates used above was within 0.04%, and as such no adjustments were made.

A series of complimentary charts regarding the spread of COVID-19 are available from the ABC website.

State-wise Comparison of Confirmed Infection Rates

ausPops <- tribble(
  ~State, ~Population,
  "New South Wales",    8117976,
  "Victoria", 6629870,
   "Queensland", 5115451,
  "South Australia", 1756494,
  "Western Australia", 2630557,
  "Tasmania", 535500,
  "Northern Territory", 245562,
  "Australian Capital Territory", 428060
)

minRate <- 4
p5 <- confirmed %>%
  dplyr::filter(
    Country == "Australia"
  ) %>%
  dplyr::rename(State = `Province/State`) %>%
  left_join(ausPops) %>%
  mutate(
    Rate = round(1e6*confirmed / Population, 2),
    Date = format.Date(date, "%d-%B")
  ) %>%
  dplyr::filter(
    !is.na(Population),
    !str_detect(State, "Territory"),
    Rate > minRate
  ) %>%
  arrange(date) %>%
  mutate(
    State = fct_inorder(State)
  ) %>%
  dplyr::rename(
    Confirmed = confirmed
  ) %>%
  ggplot(
    aes(
      x = date, y = Rate, colour = State, 
      label = Date, key = Confirmed
      )
  ) +
  geom_point() +
  geom_smooth(
    method = "lm", 
    se = FALSE,
    show.legend = FALSE
  ) +
  geom_line(linetype = 3) +
  scale_y_log10() +
  labs(
    x = "Date",
    y = "Confirmed Infection Rate (cases/million)"
  )
# Hide the tooltip from the regression lines
n <- length(levels(p5$data$State))
p5 <- ggplotly(p5, tooltip = c("Date", "Rate", "State", "Confirmed"))
regIndex <- seq(n + 1, length.out = n, by = 1)
p5$x$data[regIndex] <- lapply(
  p5$x$data[regIndex],
  function(x){
  x$hoverinfo <- "none"
  x
})

p5

Infection rates for each state with data beginning for each state once 4 confirmed cases /million was exceeded. Linear regression lines are shown for each state as solid lines, with NSW perhaps showing a slightly increased rate of infection within the population. Once again, the y-axis is on a logarithmic scale indicating exponential growth is occurring. States are shown in order of the initial date they passed 4 cases/million. Due to the low population sizes in the ACT and NT, these territories were omitted.

Statistical Analysis of State-wise Infection Rates

In order to test whether the infection rates are different between states, a linear regression model was fit. \(\log_{10}\)(Cumulative Confirmed Infection Rate) was assigned as the response variable with predictor variables being the State and Date. Each State was assigned its own intercept and slope by use of an interaction term (i.e. State:date). Given the potentially larger slope in NSW, this state was set as the baseline, with each other slope (i.e. interaction term) being presented as the difference in slope between each state and NSW. In this way comparisons against NSW were performed, but no comparisons between other states were performed.

Differences in the State-level intercepts are not particularly relevant, apart from capturing the initial time at which cumulative confirmed infection rate exceeded 4 cases / million. Differences between State-level slopes and NSW however, are of great interest, and as such only the slopes are shown. For NSW (Term = date) this captures the actual slope of the daily change in infection rate, whilst for all other States, this represents the difference between the daily change in infection rate for that State in comparison to NSW. Only differences in slope with an FDR-adjusted p-value < 0.05 are of particular interest. For those States which appear to be of interest, a negative value indicates an infection rate increasing more slowly than NSW, whilst a positive value indicates the opposite..

lm <- confirmed %>%
  dplyr::filter(
    Country == "Australia"
  ) %>%
  dplyr::rename(State = `Province/State`) %>%
  left_join(ausPops) %>%
  mutate(
    Rate = round(1e6*confirmed / Population, 2),
    Date = format.Date(date, "%d-%B")
  ) %>%
  dplyr::filter(
    !is.na(Population),
    !str_detect(State, "Territory"),
    Rate > minRate
  ) %>%
  arrange(desc(confirmed)) %>%
  mutate(
    State = fct_inorder(State)
  ) %>%
  dplyr::rename(
    Confirmed = confirmed
  ) %>%
  with(
    lm(log10(Rate) ~ (State + date)^2)
  ) 

lm %>%
  tidy() %>%
  mutate(
    FDR = p.adjust(p.value, method = "fdr"),
    term = str_remove_all(term, "State")
  ) %>%
  rename(
    Term = term,
    Estimate = estimate,
    SE = std.error,
    `T` = statistic,
    p = p.value
  ) %>%
  dplyr::filter(
    str_detect(Term, ":date")
  ) %>%
  mutate(
    Term = str_remove(Term, ":date"),
    Estimate = sprintf("%.4f", Estimate),
    SE = sprintf("%.3f", SE),
    `T` = sprintf("%.2f", `T`),
    p = case_when(
      p < 1e-4 ~ sprintf("%.2e", p),
      p >= 1e-4 ~ sprintf("%.4f", p)
    ),
    FDR = case_when(
      FDR < 1e-4 ~ sprintf("%.2e", FDR),
      FDR >= 1e-4 ~ sprintf("%.4f", FDR)
    )
  ) %>%
  pander(
    justify = "lrrrrr",
    emphasize.strong.rows = which(
      as.numeric(.$FDR) < 0.05 & .$Term != "date"
      ),
    caption = paste(
      "*Results of linear regression analysis", 
      "comparing the slopes of lines which track __daily",
      "change in cumulative confirmed infection rates__,",
      "scaled for population size in each state.",
      "Intercept terms are not shown.",
      "All states are shown in comparison to NSW.", 
      "Any highlighted state indicates an infection rate which is increasing at a different daily rate to NSW.",
      "Positive values in the Estimate column indicate a greater rate the NSW, whilst a negative value in the Estimate column indicates a slower growth rate than NSW.",
      "Diagnostic plots visually appeared",  
      "to be within acceptable bounds for real data,",
      "the fitted model passed the Shapiro-Wilk Test",
      "for normality", 
      paste0(
        "(p = ", 
        sprintf(
          "%.4f", shapiro.test(resid(lm))$p.value
        ),
        ")*."
      )
    )
  )

Results of linear regression analysis comparing the slopes of lines which track daily change in cumulative confirmed infection rates, scaled for population size in each state. Intercept terms are not shown. All states are shown in comparison to NSW. Any highlighted state indicates an infection rate which is increasing at a different daily rate to NSW. Positive values in the Estimate column indicate a greater rate the NSW, whilst a negative value in the Estimate column indicates a slower growth rate than NSW. Diagnostic plots visually appeared to be within acceptable bounds for real data, the fitted model passed the Shapiro-Wilk Test for normality (p = 0.0431).

Term	Estimate	SE	T	p	FDR
Victoria	0.0086	0.006	1.41	0.1644	0.1973
Queensland	0.0105	0.006	1.73	0.0898	0.1348
Western Australia	0.0231	0.006	3.81	0.0003	0.0010
South Australia	-0.0011	0.005	-0.23	0.8221	0.8235
Tasmania	-0.0172	0.005	-3.46	0.0010	0.0021

coef(lm) %>% 
  enframe(name = "Term", value = "coef") %>%
  dplyr::filter(str_detect(Term, "date")) %>%
  mutate(
    slope = case_when(
      str_detect(Term, "State") ~ coef[[1]] + coef,
      !str_detect(Term, "State") ~ coef
    ),
    Term = str_remove(Term, "State"),
    State = str_remove(Term, ":date"),
    State = str_replace(State, "date", "New South Wales")
    ) %>%
  left_join(
    confirmed %>% 
      dplyr::filter(
        Country == "Australia", 
        date == max(date)
      ) %>% 
      rename(State = `Province/State`) %>%
      dplyr::select(State, date, confirmed)
  ) %>%
  mutate(
    predicted = round(10^slope*confirmed, 0),
    slope = percent(10^slope, accuracy = 0.1),
  ) %>%
  dplyr::select(
    State, 
    `Expected Daily Increase` = slope,
    `Most Recent` = confirmed,
    `Predicted For Next Day` = predicted
    ) %>%
  pander(
    justify = "lrrr",
    caption = paste(
      "Results from linear regression shown as the",
      "expected daily increase in cases for the",
      "current exponential growth phase.",
      "Most recent values were taken from the official",
      "figures on",
      confirmed %>%
        dplyr::filter(Country == "Australia") %>%
        .[["date"]] %>%
        max() %>%
        format("%d %B, %Y."),
      "Predictions are for",
      confirmed %>%
        dplyr::filter(Country == "Australia") %>%
        .[["date"]] %>%
        max() %>%
        add(1) %>%
        format("%d %B, %Y."),
      "Standard errors for predictions have not been included."
    )
  )

Results from linear regression shown as the expected daily increase in cases for the current exponential growth phase. Most recent values were taken from the official figures on 22 March, 2020. Predictions are for 23 March, 2020. Standard errors for predictions have not been included.

State	Expected Daily Increase	Most Recent	Predicted For Next Day
New South Wales	121.1%	533	645
Victoria	123.5%	278	343
Queensland	124.0%	221	274
Western Australia	127.7%	130	166
South Australia	120.8%	67	81
Tasmania	116.4%	16	19

Assessment of Testing Within Each State

Testing numbers were originally sourced from https://covid-19-au.github.io/, then were automatically updated should any later figures be provided at https://api.infotorch.org/api/covid19/totals/. The number of tested individuals in each state was then assessed as a function of State population size. All results are valid at the time of report generation, however these numbers are initially dependent on media releases and may lag actual testing numbers by 24-48 hours.

tribble(
  ~State, ~Tested, 
  "New South Wales", 40651, 
  "Queensland", 29579,
  "Victoria", 19337,
  "Western Australia", 8603,
  "South Australia", 13000,
  "Tasmania", 807,
  "Australian Capital Territory", 2062
) %>%
  left_join(
    latestAU, 
    by = c("State"  = "Province/State")
    ) %>% 
  rowwise() %>% 
  mutate(
    Tested = max(Tested, tested, na.rm = TRUE)
    ) %>% 
  ungroup() %>% 
  dplyr::select(State, Tested) %>%
  left_join(
    confirmed %>%
      dplyr::filter(
        date == max(date)
      ) %>%
      rename(
        State = `Province/State`
      )
  ) %>%
  left_join(ausPops) %>%
  mutate(
    `Percent Tested` = Tested / Population,
    Positive = confirmed / Tested,
    Negative = 1 - Positive
  ) %>%
  dplyr::select(
    State, Population, `Total Tested` = Tested, contains("Percent"), ends_with("ive")
  ) %>%
  arrange(desc(`Percent Tested`)) %>%
  mutate_at(
    vars(contains("Percent"), ends_with("ive")),
    percent,
    accuracy = 0.01
  ) %>%
  pander(
    justify = "lrrrrr",
    caption = paste(
      "*COVID-19 testing scaled by State population size.",
      "Confirmed cases are assumed to be the tests",
      "returning a positive result.",
      "The current numbers available for SA are a", 
      "lower limit, so in reality, the proportion of",
      "the population tested is higher, as is the",
      "proportion of tests returning a negative result.*"
    )
  )

COVID-19 testing scaled by State population size. Confirmed cases are assumed to be the tests returning a positive result. The current numbers available for SA are a lower limit, so in reality, the proportion of the population tested is higher, as is the proportion of tests returning a negative result.

State	Population	Total Tested	Percent Tested	Positive	Negative
South Australia	1,756,494	13,000	0.74%	0.52%	99.48%
New South Wales	8,117,976	52,663	0.65%	1.01%	98.99%
Queensland	5,115,451	29,867	0.58%	0.74%	99.26%
Australian Capital Territory	428,060	2,221	0.52%	0.86%	99.14%
Western Australia	2,630,557	8,603	0.33%	1.51%	98.49%
Victoria	6,629,870	19,337	0.29%	1.44%	98.56%
Tasmania	535,500	807	0.15%	1.98%	98.02%

R Session Information

R version 3.6.3 (2020-02-29)

Platform: x86_64-pc-linux-gnu (64-bit)

locale: LC_CTYPE=en_AU.UTF-8, LC_NUMERIC=C, LC_TIME=en_AU.UTF-8, LC_COLLATE=en_AU.UTF-8, LC_MONETARY=en_AU.UTF-8, LC_MESSAGES=en_AU.UTF-8, LC_PAPER=en_AU.UTF-8, LC_NAME=C, LC_ADDRESS=C, LC_TELEPHONE=C, LC_MEASUREMENT=en_AU.UTF-8 and LC_IDENTIFICATION=C

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: plotly(v.4.9.2), pander(v.0.6.3), jsonlite(v.1.6.1), glue(v.1.3.1), broom(v.0.5.4), ggrepel(v.0.8.1), matrixStats(v.0.55.0), scales(v.1.1.0), lubridate(v.1.7.4), magrittr(v.1.5), forcats(v.0.4.0), stringr(v.1.4.0), dplyr(v.0.8.4), purrr(v.0.3.3), readr(v.1.3.1), tidyr(v.1.0.2), tibble(v.2.1.3), ggplot2(v.3.2.1) and tidyverse(v.1.3.0)

loaded via a namespace (and not attached): httr(v.1.4.1), viridisLite(v.0.3.0), modelr(v.0.1.6), shiny(v.1.4.0), assertthat(v.0.2.1), highr(v.0.8), cellranger(v.1.1.0), yaml(v.2.2.1), pillar(v.1.4.3), backports(v.1.1.5), lattice(v.0.20-40), digest(v.0.6.25), promises(v.1.1.0), rvest(v.0.3.5), colorspace(v.1.4-1), htmltools(v.0.4.0), httpuv(v.1.5.2), pkgconfig(v.2.0.3), haven(v.2.2.0), xtable(v.1.8-4), later(v.1.0.0), generics(v.0.0.2), farver(v.2.0.3), ellipsis(v.0.3.0), withr(v.2.1.2), lazyeval(v.0.2.2), cli(v.2.0.1), crayon(v.1.3.4), readxl(v.1.3.1), mime(v.0.9), evaluate(v.0.14), fs(v.1.3.1), fansi(v.0.4.1), nlme(v.3.1-144), MASS(v.7.3-51.5), xml2(v.1.2.2), Cairo(v.1.5-10), tools(v.3.6.3), data.table(v.1.12.8), hms(v.0.5.3), lifecycle(v.0.1.0), munsell(v.0.5.0), reprex(v.0.3.0), compiler(v.3.6.3), rlang(v.0.4.4), grid(v.3.6.3), rstudioapi(v.0.11), htmlwidgets(v.1.5.1), crosstalk(v.1.0.0), labeling(v.0.3), rmarkdown(v.2.1), gtable(v.0.3.0), DBI(v.1.1.0), curl(v.4.3), R6(v.2.4.1), zoo(v.1.8-7), knitr(v.1.28), fastmap(v.1.0.1), stringi(v.1.4.6), Rcpp(v.1.0.3), vctrs(v.0.2.3), dbplyr(v.1.4.2), tidyselect(v.1.0.0) and xfun(v.0.12)

Report prepared by the University of Adelaide, Bioinformatics Hub. https://www.adelaide.edu.au/bioinformatics-hub/